Hey! So I'm thinking about this one too. FYI: Airbnb is totally your friend if you stay in NYC. Think Harlem or the Bronx and you can get good deals. Just pay attention to reviews.
From NYC to New Haven on Metronorth is ~2hrs, cost $43.50 roundtrip, and you'll want to be at the Harlem-125th Station at around 7:45 to make sure you've sorted out your ticket so you can leave on the 8:14 train, arriving at 10:09 in New Haven, and taxi over ($$$?) to North Haven for the interview which I assume, like mine, starts at 10:45. Me, I might even err on the side of caution and take the 7:40 train that arrives at 9:27 since I have no idea what the taxi situation is like in New Haven on interview days.
But I think I do recommend this since it's actually about 2hrs and 20 minutes by car from West Harlem, where I live. It'll most likely be faster, easier, and cheaper than trying to locate a low priced rental place, getting there, paying tolls, gas, finding parking, etc. It's what I'm going to do.
In other news, if you're on a budget and want to visit bars, I recommend visiting the West 4th area, which is a nice mix of cheap for college students but super NYC because the college students are attending NYU.
If you're looking for cheap, unusual, arty, and very NYC fun, follow theskint.com. Good stuff there. Cheap broadway tickets at TKTS in Times Square.